pose there arenpeople in a group, each aware of a scandal no one else in the group knows about. These people communicate by telephone; when two people in the group talk, they share information about all scandals each knows about. For example, on the first call, two people share information, so by the end of the call, each of these people knows about two scandals, Thegossip problemasks forG(n), the minimum number of telephone calls that are needed for allnpeople to learn about all the scandals. Exercises 69-71 deal with the gossip problem.
*72.Show that if is possible to arrange the numbers 1,2,.. .,nin a row so that the averag of any two of these numbers number never appears between them, [Hint: Show
that it suffices to prove this fact whennis apower of 2. Then use mathematical induction to prove the result whennis apower of 2.]
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